Hist(yrical Note on the Method oj Least Squares. 415 



The article closes on p. 109 of tlie Analyst with the following : 



" I have applied the principles of this essav to the determin- 

 ation of the most probable value of the earth's ellipticity, &c., 

 but want of room will not permit me to give the investigation 

 at this time." 



The investigations here alluded to were, however, long after- 

 wards published, i. e., in 1817, in vol. i, new series, of the 

 Transactions of the American Philosophical Society, and are 

 given in two papers (Nos. IV and XXVIII) of that volume. 

 The preceding note as w-ell as the dates written on the manu- 

 scripts (which are still preserved by the Hon. G. B. Adrian of 

 New Brunswick) show that these two investigations were com- 

 pleted in 1808. 



The first of the papers here alluded to is entitled " Investiga- 

 tion of the figure of the earth and of the gravity in different 

 latitudes," from which as printed in the Phil. Trans., we make 

 the following extract : 



"Having in the year 1808 discovered a general method ol 

 resolving several useful problems by ascertaining the highest 

 degree of probability, when certainty cannot be found, I shall 

 here apply that method to the determining of the earth's elhp- 

 ticity, &c." The author's computation is based on the lengths 

 of the seconds pendulum as given by Laplace (Mec. Cel^ m), 

 and having stated the problem before him, he says: "This is 

 accomplished by a rule published by the writer in the Analyst, 

 m 1808." The resulting ellipticity (3K) he shows to chtter 

 from that deduced by Laplace (gi^j because of numerical errors 

 m the computation of the latter ; having corrected these he 

 deduces the ellipticity 3^-5 by Laplace's own method— show- 

 ing that the two methods conduce to nearly the same result.^^ 



The second of the articles in the Phil Trans., is entitled A 

 Research concernincr the Mean Diameter of the lliarth. in 

 this the author seeks the sphere which most nearly coincides m 

 various specified peculiarities with the actual terrestrial spheroia , 

 the diameter of this sphere he determines to be 7918-/ miies. 

 This numerical result is based upon some eariier computations, 

 the details of which are not given, but of which he savs 

 ■'Having detennined the most probLble axis of the terres rial 

 Jpheroid from the measurements of a degree of the meiuiu 

 bv a method which I discovered several years ago and pub- 

 [^shed in the Analyst, the resulting mean radms was found to 

 be 3959.69 English miles." ^ , , . ,,, ,„ 



The mathematical works published by Dr. ^<^"^f J'^^'^ 

 ^ely to be met with, that it was necessary to make these long 

 extracts in order to establish the conclusion t^.^X indenen 

 ^"^ved, i. e., that we must credit Dr. Adrian with the mdepen 

 ?ent invention and application of the ^5?* f^'^^^^^" of the 



^ process that has been invoked to aid the progress of the 



exact 



sciences. 



"Washington, 



